Given an array of n integers, your task is to find all integers that are the xor sum in some subarray.

Input

The first line has an integer n: the size of the array.

The next line has n integers x_1,x_2,\dots,x_n: the contents of the array.

Output

First print an integer k: the number of distinct integers that are the xor sum in some subarray.

After this print k integers: the xor sums in increasing order.

Constraints

• 1 \le n \le 2 \cdot 10^5
• 0 \le x_i \le 10^6

Example

Input:

4
5 1 5 9

Output:

7
1 4 5 8 9 12 13